Direct approximation
A patent interval in a given EDO is the number of EDO steps needed to reach the best approximation of a given interval – usually, but not necessarily just – in that EDO. The method for calculating patent intervals is referred to as direct mapping, and it involves rounding the product of the binary logarithm (log2) of the interval ratio (r) and the EDO number (nEdo).
round(log2(r)*nEdo)
- Some Examples
| \ | 12edo | 17edo | 19edo | 26edo |
|---|---|---|---|---|
| 3/2 | 7 | 10 | 11 | 15 |
| 5/4 | 4 | 5 | 6 | 8 |
| 6/5 | 3 | 4 | 5 | 7 |
| 7/4 | 10 | 14 | 15 | 21 |
A patent val is the best mapping of a representative set of intervals (taken to be generators for a JI subgroup) in a given EDO; for the p-prime limit this set consists of prime intervals. Just as the patent val itself can be referred to as the "nearest edomapping", so a patent interval can be referred to as a "direct mapping".